Study of SX-682 Plus Enzalutamide in Men With ARPI-Resistant Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: 1. Signed and dated Institutional Review Board (IRB)/Independent Ethics Committee (IEC)-approved informed consent form prior to beginning study and undergoing procedures. 2. 2\. Diagnosis of mCRPC with (a) any histology, and (b) currently on or previously on abiraterone/prednisone (or abiraterone/dexamethasone) or darolutamide, apalutamide or enzalutamide with documented progression in either the mCRPC or mHSPC settings, and currently with: * rising PSA (a rising PSA requires at least 3 measurements obtained at least 1 week apart showing increase from nadir with the last level above 2 ng/mL by local testing); or * progression of new or existing bone or soft tissue metastatic lesions by CT, MRI or bone scan; no washout necessary. 3. Availability of archival tumor tissue for pathologic review and correlative studies. Tumor tissue (localized or metastatic) does not need to be received but rather identified and available (slides and blocks) upon later request for future pathologic review and possible correlative studies. 4. Castrate levels of serum total testosterone (\<50 ng/dl) OR ongoing documented ADT. 5. Karnofsky performance status of 70 or higher. 6. ≥ 18 years of age 7. Life expectancy of ≥ 6 months 8. Recovered to ≤ Grade 2 toxicity from prior therapy (per CTCAE Version 5.0) 9. Adequate bone marrow function: * Absolute neutrophil count (ANC) ≥ 1.2 × 10\^9/L without any growth factors in prior 7 days * Hemoglobin ≥ 9.0 g/dL with no blood transfusion in the prior 14 days * Platelet count ≥ 75 × 10\^9/L with no platelet transfusion in the prior 7 days Adequate hepatic function: * Total bilirubin ≤ 1.5 × ULN (≤ 3 × ULN for Gilbert's syndrome) * AST (serum glutamic oxaloacetic transaminase \[SGOT\]) / ALT (serum glutamic pyruvate transaminase \[SGPT\]) ≤ 3 × institutional ULN Adequate renal function: \- Creatinine clearance per Cockcroft-Gault equation (or institutional equivalent) of ≥ 50 mL/min 10. Willingness of patients who are not surgically sterile or with partners who are not postmenopausal to use medically acceptable methods of birth control for the duration of the study treatment, including 90 days after the last dose of study drug. 11. Willing and able to provide written informed consent and HIPAA authorization for the release of personal health information. Exclusion Criteria: 1. Prior systemic anticancer treatment: * Prior treatment with docetaxel or marketed antibody within 4 weeks of first dose of study treatment * Prior radium-223 therapy within 6 weeks * Prior PSMA-Lu177-617 therapy within 4 weeks 2. 2\. Prior receipt of (a) ketoconazole, (b) 2 or more chemotherapy regimens with docetaxel or (c) any chemotherapy other than docetaxel. 3. Current presence of liver metastases on imaging. 4. Has received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. 5. Major surgery requiring general anesthesia within 3 weeks of starting study treatment (limited biopsy or line placement is acceptable) 6. Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. 7. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. 8. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 9. Congestive heart failure (New York Heart Association Class III or IV) or unstable angina pectoris; previous history of myocardial infarction within one year prior to study entry, uncontrolled hypertension, or uncontrolled arrhythmias. 10. Has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. 11. Has known active untreated CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment greater than prednisone 10 mg daily (or equivalent) for at least 14 days prior to first dose of study intervention. 12. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. 13. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 14. Has an active infection requiring systemic therapy. 15. Has a known uncontrolled Human Immunodeficiency Virus (HIV) infection based on detectable HIV viral load and abnormal CD4 count of \<350/mm\^3. 16. Has a known active Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. 17. Has a known active TB (Bacillus Tuberculosis) infection. 18. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 19. Has known current psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 20. Has had an allogenic tissue/solid organ transplant. 21. Concomitant medication(s) known to be (a) a strong inhibitor or inducer of CYP3A4, or (b) QT prolonging as defined in the drug's approved label, with the exception of drugs that are considered absolutely essential for the care of the subject or if the Investigator believes that beginning therapy with such medication is vital to an individual subject's care while on study, and in either case, there is no alternative drug (if exceptions apply contact Syntrix medical monitor prior to enrollment). 22. ECG demonstrating a QTcF interval \> 470 msec or patients with congenital long QT syndrome. 23. Coronary artery bypass, angioplasty, vascular stent, myocardial infarction, angina or congestive heart failure in the last 6 months.